Methods for accurate use of finite dynamic range measurement data in radio path loss propagation model calibration

ABSTRACT

Methods for accurately predicting radio propagation from signal strength measurements. Dynamic range limitations in the measurement data are explicitly taken into account. The resulting propagation models accurately predict signal strength for calculation of coverage and interference.

CLAIM OF PRIORITY

U.S. Provisional Patent Application No. 60/661,128 entitled Methods for Accurate Use of Finite Dynamic Range Measurement Data in Radio Path Loss Propagation Model Calibration, by Nathan Hunt et al., filed Mar. 11, 2005.

COPYRIGHT NOTICE

A portion of the disclosure of this patent document contains material that is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the U.S. Patent and Trademark Office patent file or records, but otherwise reserves all copyright rights whatsoever.

FIELD OF THE INVENTION

This invention relates to the field of calibrating data parameter sets for application to a signal propagation model describing data of limited dynamic range.

BACKGROUND OF THE INVENTION

The effectiveness of predictive design and optimization of cell phone networks depends on the accuracy of predicted radio signal strength over the geographic area where service is to be provided. The prediction is made with a mathematical model called a propagation model. Propagation models typically predict radio signal strength given the transmitting antenna pattern and digital terrain maps and clutter maps, although they may also use additional descriptions of the physical environment such as vector data and building databases. Propagation models have a number of parameters whose values are determined by calibrating the model with measurement data. Once a model is calibrated for a particular geographic area, the required signal strength and interference predictions can be carried out.

Model calibration is required to give specific loss characteristics to the physical environment description. For example, the average properties of clutter categories may vary between markets or be unknown altogether. Model calibration assigns optimal values to each clutter category.

The signal strength measurement data used for model calibration is usually either Continuous Wave (CW) data or scanner data. To collect CW data, a clear frequency is selected and a continuous signal is transmitted at that frequency. Data is collected over a drive route. A receiver set to the transmitting frequency collects the data in conjunction with position information from a GPS receiver.

Scanner data is also collected on a drive with simultaneous collection of GPS data. Scanner data is distinct from CW data in that the actual pilot signals from the network are detected, rather than the separate monotone signal used for CW. Signals can be collected from many sites simultaneously, depending on the scanner configuration.

Model calibration is conventionally carried out by finding the parameter set that gives the minimum least-squares (or OLS, for Ordinary Least Squares) fit to the measurement data. Under certain simple assumptions (i.e. that the errors in the data are normally distributed, and that data is an unbiased sample of the underlying population), the OLS fit is the best prediction that can be made.

All measurement data has a finite dynamic range. This generally introduces bias into the measurement data set. Models created by OLS fit to the data may therefore be biased and will not give the best prediction possible.

The effects of the bias due to finite dynamic range are shown in FIGS. 1 and 2. In FIG. 1, received signal strength is shown as a function of distance, along with a simple linear OLS fit to the data. In FIG. 2, the same data set is shown, this time with signals below −100 dBm excluded. The resulting OLS fit predicts less attenuation with distance than does the fit to the full data set shown in FIG. 1. While the OLS fit in FIG. 2 fully reflects the bias in the measurement data set, the Maximum Likelihood (ML) fit (described below) corrects for this bias and gives results nearly equal to those obtained with the full data set.

The example data in FIGS. 1 and 2 is artificial in that the truncation level was applied to the data set, rather than being an inherent feature of it. In real applications, the truncation level or levels are inherent in the data and must be explicitly included in a ML model, as described below. Additionally, a propagation model is usually more complicated than the simple linear fits shown in FIGS. 1 and 2, and will incorporate diffraction and clutter effects among others, as well as antenna discrimination where appropriate. But the figures serve to illustrate the basic issue of bias introduced by limited dynamic range.

SUMMARY OF THE INVENTION

The invention consists of approaches to calibrating propagation models that removes the bias inherent in using data that is of limited dynamic range. It also covers means of implementing these methods in software.

The invention describes treating two types of measurement data, truncated data and censored data. Truncated data is data where observations outside of given limits are lost. A simple example of truncated data is shown in FIG. 2, where measurements with values below −100 dBm are not present in the data set. Data may be truncated from below, above, or both. The truncation level or levels may also vary across the data set.

Censored data is similar to truncated data, the difference being that the location of the points falling outside the receiver dynamic range is given. For example, in the case of the data in FIG. 2, if additionally the distance to each of the observations falling below −100 dBm were known, these would be called censored observations (or left-censored, since they are below a known value). As is the case with truncated data, data may be censored from above (right censored), from below (left censored), or both, and the censoring levels need not be constant across the data set.

The invention describes how to obtain truncated data and truncation levels from measurement data. It also describes how to obtain censored data, censoring levels, and censored observations from measurement data. It describes how to obtain optimal models for truncated and censored data sets using Maximum Likelihood (ML).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a chart measuring signal vs. log of distance with an OLS linear fit.

FIG. 2 is a chart measuring signal vs. log of distance, signal level truncated at −100 dBm, with the OLS and truncated ML linear fits to the truncated data. The ML fit corrects for the bias introduced by the truncation, and gives a result quite close to the OLS fit to the full data set shown in FIG. 1.

FIG. 3 is a flow diagram for truncated CW data.

FIG. 4 is a flow diagram for truncated scanner data.

FIG. 5 is a flow diagram for censored CW data.

FIG. 6 is a flow diagram for censored scanner data.

DETAILED DESCRIPTION OF THE INVENTION

CW measurements can be treated as truncated data by using the signal sensitivity threshold as the lower truncation level, and the top end of the receiver linear range as the upper truncation level. Any observations outside these limits are excluded from the data set. FIG. 3 shows a flow diagram of this process.

Scanner data can be treated as truncated data by excluding measurements above the linear range or below the receiver sensitivity. The sensitivity limit for scanner data differs from the limit for CW data in that, for scanner data, the sensitivity is often limited by interference. Therefore the lower truncation levels are determined from the interference level measured at each data point. The lower truncation level at a point in the case of CDMA or UMTS is the measured value of I₀ (in dBm) at a point plus the minimum Ec/I₀ (in dB) that the scanner can reliably measure. For the case of GSM data, the lower truncation level is the measured value of I (in dBm) at a point plus the minimum value of C/I (in dB) that the scanner can reliably measure. FIG. 4 shows a flow diagram of this process.

Given a truncated data set, the optimum propagation model is obtained as follows.

To help define notation, we start by giving the formulation for the OLS solution. Vector quantities are shown in bold. The OLS solution is given by finding the vector β minimizing the quantity Σ(y _(i) −x _(i)β)²  (1) where the sum is taken over all observations i, y_(i) is the i^(th) measured value, x_(i) is a vector of the variables used in the calibration (the dependent variables, such as log distance, diffraction, effective antenna height, clutter terms, etc.), and β is a vector of the parameters to be optimized (constant term or intercept, slope, diffraction multiplier, clutter parameters, etc).

The OLS problem can be reformulated as a maximum likelihood (ML) problem, where the log of the likelihood to be maximized is L=Σ _(i) log (2 π σ)^(−1/2)−Σ_(i)(y _(i) −x _(i)β)²/(2 σ²)  (2) where y_(i), x_(i) and β are as in equation (1) and σ, an estimate of the dispersion, is an additional model parameter to be optimized along with the components of β. The maximum likelihood solution of (2) will yield the same solution β as (1), with the optimum value of σ equal to the standard deviation of the measurements, y_(i).

The optimum parameter set for the truncated problem is obtained by maximizing the log of the likelihood (Tobin, Breen) L, L=Σ _(i) log (2 π σ)^(−1/2)−Σ_(i)(y _(i) −x _(i)β)²/(2 σ²) −Σ_(i) log Φ[(c _(i) −x _(i) β)/σ]−Σ_(i) log Φ[(x _(i) β−d _(i))/σ]  (3) where y_(i), x_(i) β and σ are as in (2), the c_(i) are the upper truncation values, the d_(i) are the lower truncation values, and Φ is the standard normal distribution function (Breen).

Censored data can be generated from CW data by using the positions of points where the measurement falls below the sensitivity limit of the receiver (left censored observations) or above the receiver's linear range (right censored observations). Censored data is generated from scanner data in the same way, but the lower limit is usually determined by the measured interference at each point. The lower censoring level at a point in the case of CDMA or UMTS is the measured value of I₀ (in dBm) at a point plus the minimum Ec/I₀ (in dB) that the scanner can reliably measure. For the case of GSM data, the lower censoring level is the measured value of I (in dBm) at a point plus the minimum value of C/I (in dB) that the scanner can reliably measure.

FIG. 5 shows a flow diagram of the process for censored CW data, while FIG. 6 shows a flow diagram of the process for censored scanner data.

The optimum parameter set for the censored problem is obtained by maximizing the log of the likelihood, L L=Σ _(i) log (2 πσ)^(−1/2)−Σ_(i)(y _(i) −x _(i)β)²/(2 σ²)−Σ_(j) log Φ[(x _(j) β−c _(j))/σ]−Σ_(k) log Φ[(d _(k) −x _(k) β)/σ]  (4) where the summations over i are sums over the uncensored observations, the summations over j are over the right-censored observations, the summations over k are over the left-censored observations, y_(i), x_(i), β and σ are as in (3), c_(j) and d_(k) are the upper and lower censoring limits, respectively, and x_(k) is the vector of dependent variables at the k^(th) censored observation.

REFERENCES

Breen, R. (1996) Regression Models: Censored, Sample Selected, or Truncated Data. Thousand Oaks: Sage Publications

Tobin, J. (1958) “Estimation of relationships for limited dependent variables.” Econometrica 26: 24-36 

1. A method of accurately calculating an optimal parameter set for application to a signal propagation model describing data of limited dynamic range, comprising the steps of: a) representing a set of N data points collected by a receiver as a truncated data set, wherein said truncated data set is truncated using a set of N lower truncation limits, wherein a lower truncation limit is calculated for each data point according to a sensitivity threshold of said receiver, and wherein said truncated data set is further truncated using an upper truncation limit calculated according to an upper limit of the linear range of said receiver; b) excluding from said truncated data set all data outside a range defined by said lower and upper truncation limits; and c) based on said truncated data set, based on said lower and upper truncation limits, and based on a given signal propagation model, calculating an optimal parameter set maximizing the accuracy with which said signal propagation model describes said data set.
 2. The method of claim 1, wherein said step of calculating comprises maximizing the likelihood of said signal propagation model given said data, said lower truncation limit, and said upper truncation limit.
 3. The method of claim 1, wherein said data is radio signal data.
 4. The method of claim 1, wherein said data is microwave signal data.
 5. The method of claim 1, wherein said data is signal strength data.
 6. The method of claim 1, wherein said data pertains to a cellular phone network.
 7. The method of claim 1, wherein said data is cellular phone signal strength data.
 8. The method of claim 1, wherein said step of calculating is performed using a maximum likelihood (ML) fit.
 9. The method of claim 1, wherein said receiver is one of a CDMA radio scanner and a UMTS radio scanner, and wherein the lower truncation limit is calculated at each data point by adding the minimum detectable Ec/I₀ at said data point to the measured I₀ at said data point.
 10. The method of claim 1, wherein said receiver is a GSM radio scanner, and wherein the lower truncation limit is calculated at each data point by adding the minimum detectable C/I at said data point to the measured I at said data point.
 11. A method of accurately calculating an optimal parameter set for application to a signal propagation model describing data of limited dynamic range, comprising the steps of: a) representing a set of data points collected by a receiver as a censored data set, wherein said censored data set comprises a set of uncensored observations, a set of left-censored observations, and a set of right-censored observations; b) defining the set of uncensored observations as all measured data points with signal level within the linear range of said receiver; c) defining the set of right-censored observations as the set of all measured points with a measured signal level above the receiver's linear range; d) defining the set of left-censored observations as the set of all signals not detected due to being below the minimum detection level of the receiver; e) defining an upper censoring limit as equal to the upper limit on the linear range of said receiver; f) defining a lower censoring limit as equal to the minimum detection level of said receiver; and g) based on said censored data set, based on said lower and upper censoring limits, and based on a given signal propagation model, calculating an optimal parameter set maximizing the accuracy with which said signal propagation model describes said data set.
 12. The method of claim 11, wherein said step of calculating comprises maximizing the likelihood of said signal propagation model given said data, said lower censoring limit, and said upper censoring limit.
 13. The method of claim 11, wherein said data is radio signal data.
 14. The method of claim 11, wherein said data is microwave signal data.
 15. The method of claim 11, wherein said data is signal strength data.
 16. The method of claim 11, wherein said data pertains to a cellular phone network.
 17. The method of claim 11, wherein said data is cellular phone signal strength data.
 18. The method of claim 11, wherein said step of calculating is performed using a maximum likelihood (ML) fit.
 19. The method of claim 11, wherein said receiver is one of a CDMA radio scanner and a UMTS radio scanner, and wherein a set of left-censored observations is defined at each geographic point where signals were detected, by examining the set of all detected signals and adding left-censored observations for all signals that were not detected, using a lower censoring limit obtained by adding the minimum detectable Ec/I₀ for said data point to the measured I₀ for said data point.
 20. The method of claim 11, wherein said receiver is a GSM radio scanner, and wherein a set of left-censored observations is defined at each geographic point where signals were detected, by examining the set of all detected signals and adding left-censored observations for all signals that were not detected, using a lower censoring limit obtained by adding the minimum detectable C/I for said data point to the measured I for said data point. 